I play disc priest myself and in that kind of fight, where people might take alot of damage that they shouldn't (this is often about learning the mechanics like the smoke of death) spirit shell and absorb mechanics come really handy.

Over the 7 minute encounter he/she popped SS only once. In this encounter I pop it almost on cd, or at least for beam and spectrum phases. It might account for overhealing but when it comes to progression, it is better to play safe than be sorry.

Slice and Dice is the single most important buff rogues have, and anything less than 99.9% uptime is absolutely TERRIBLE. Same thing for Rupture; single most important debuff rogues have, and it should NEVER fall of for more than a second.

Quick tips for DRAMATICALLY improving DPS, because the rogue you have right now should be ashamed of himself/herself:

1. Cast Slice and Dice at the beginning of the fight, Envenom will refresh it for the rest of the fight.
2. Use Anticipation to generate combo points for free Ruptures; if you have less than 5 seconds left on the duration, get ready to spend combo points to refresh it
3. Use your damn cooldowns
4. Get RoguePowerBars
5. Stop standing in fire

Yeah it really looks like your rogue has some UI problems. Or lack of a UI in general--obviously arent watching their buff/debuff/cooldown/etc timers. Or are trying to watch the default UI and are then standing in fire? I dont know.

The Envenom uptime should be close to 50%, not hovering around 12%. Wait for your envenom to fall off before reapplying unless you are full of anticipation charges and are going to energy cap.

On nearly every parse, Blood Plague disease uptime is bad. Blood Plague lags behind his Frost Fever uptime by 20-30%. His Frost Fever and Blood Plague uptime should be within a half a percent of each other on every fight except a fight that has a lot of add cleave where he might spam howling blast (Tortos bat duty for example). Disease uptime is IMPORTANT because Obliterate hits harder by 12.5% for each disease on the target.

He rarely uses Raise Dead. This is free dmg on a 2minute CD.
He's ok at Pillar of Frost usage but he isn't always using it on CD which means he could use it more times. My suggestion, have him macro Raise Dead and Pillar of Frost together.

I think he could probably use Soul Reaper more often. This is just my gut feeling from comparing his parses to my own.

These things are all pretty easy fixes and will increase his dps. My guess is that his UI is not designed to help him as well as it could. It's not that he doesn't know to put diseases up, it's that their uptime should be better. It's also not that he doesn't use Soul Reaper, it's that he could use it more. Same with Pillar of Frost. To me, those things indicate that his UI doesn't track these things as clearly as it could.